Why depth map renderings stored in 16-bit PNG turn out to be 8-bit?
It doesn't matter what the bit depth is if the format is output referred. 32, 16, and 8 bit integer, and even in float instances, may result in output referred ranges, typically 0.0 to 1.0. In these instances, the bit depth doesn't increase the range, merely the number of steps between them.

The only real option would be a float format that supports deeper data ranges such as EXR or TIFF. Blender's TIFF support did not appear to support float instances when last examined, and even if it did it may be bound to output referred ranges.